Maths-
General
Easy
Question
An insulated collar is made to cover a pipe. Find the volume of the material used to make the collar. Let r = 3 inches, R = 5 inches and h = 21 inches.
Hint:
Subtracting volume with r from the volume with R, we will get the volume of the material.
The correct answer is: of the material used to make the collar The volume is 1056 cubic inches.
Explanations:
Step 1 of 2:
Given, r =3 inches, R =5 inches and h= 21 inches
Volume with collar = ![pi R squared h equals pi 5 squared cross times 21](data:image/png;base64,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)
Volume without collar = ![pi r squared h equals pi 3 squared cross times 21](data:image/png;base64,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)
Step 2 of 2:
Volume of material used = volume with collar – volume without collar
![equals pi cross times 21 cross times open parentheses 5 squared minus 3 squared close parentheses](data:image/png;base64,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)
![equals 22 over 7 cross times 21 cross times 8 cross times 2](data:image/png;base64,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)
cubic inches
Final Answer:
of the material used to make the collar The volume is 1056 cubic inches.
Related Questions to study
Maths-
Find the slope and write the equation of the given line.
Find the slope and write the equation of the given line.
Maths-General
Maths-
Find the value of p so that
![left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAAARCAYAAABgiRiOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAqhJREFUeNrtWjFIAzEUPYp0Ehdxcugi0kFKQUSKuIqDkyAi4iCCiBQHV+koiJODi4iIq4ODgwjiICJFEBEHEUHEWZDiVErh/IGvnCWX5CfxILl78Jbjevfea3L5+SQI3EGIbAEfgBNBhiybf8xhFbhlSVgZeKPxuy3UIUIR+G5Bhyt+KaBkk42RGJSAdYuh7QPnNX97g3rikAN+GupwyS8FlGzSOEaegbPAe2ADeAvs5z28LHj4FC5BKugDvqEg3jLGYxTDwOuYZ/cCd4GLBjpc8ksBJRvdAejyGGHvagM3IxNgDrhHWa66gU8EoxvAWkxNp4prNMwLasFQh2t+ZQNDJxvbJY0LY2QUeNVxbRJ4Er2wDawKXspmzpKi0BzO+D5Do2sxtWkPzuxlAx0u+aVANRsd+DBGWHl01HGNrQyH0QvnwPGYF44BLwlC2cMPBLt9VVQi7+WhaaDDRb8UNP9hMvgwRnZwUkdxhJPkF1/APOdh7NojsEAQylu6dIzmURcP7E+5M9Dhml8KZNmECvQhM14OrBx6jUzqIq5Qf3y1BS2sKkGorK786QEzA2fAdaw149Di/IlN/EoVDHS44JcCSja68GGMfOAEeMFO0ylwUMVoiSNaZlS1VdaFX4YatrqKlgeHTIdvfpOA65mxr39D5UbeEsj6rwMEo6I2pggTnB2+SdmgosMnv7qriI0yyaXMWNfoWOXGC9wEUUJTbZXpbvh0N5QqOnzymxRSk5msbSab9aJWmQxDuKnpRJWz8zdp2fnoN0mkJjPVMyKhRqusczdfwWByuHQxk9PEjkNgqMMXv0kiVZnVA/n5mFCjVRbFDO7k27ibZzXcCOc+3eMJlHB88Js0UpOZ7UNYJrB5cC3zm2WmhZXA3vFck9p0OaF3pc1vlpkA35KIjGCzyG3dAAABY3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bW4+NDwvbW4+PG1vPi88L21vPjxtbj41PC9tbj48bXN1cD48bW8+KTwvbW8+PG1uPjM8L21uPjwvbXN1cD48bW8+LzwvbW8+PG1vPig8L21vPjxtbj40PC9tbj48bW8+LzwvbW8+PG1uPjU8L21uPjxtc3VwPjxtbz4pPC9tbz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48L21yb3c+PC9tc3VwPjxtbz49PC9tbz48bW8+KDwvbW8+PG1uPjQ8L21uPjxtbz4vPC9tbz48bW4+NTwvbW4+PG1zdXA+PG1vPik8L21vPjxtcm93Pjxtbj4zPC9tbj48bWk+cDwvbWk+PC9tcm93PjwvbXN1cD48L21hdGg+6gbHfAAAAABJRU5ErkJggg==)
Find the value of p so that
![left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent](data:image/png;base64,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)
Maths-General
Maths-
The diameter of a cylinder is 7 yards. The height is 12 yards. What is the volume in terms of π and to the nearest cubic yard of the cylinder?
The diameter of a cylinder is 7 yards. The height is 12 yards. What is the volume in terms of π and to the nearest cubic yard of the cylinder?
Maths-General
Maths-
Which of the following lines pass through origin?
Which of the following lines pass through origin?
Maths-General
Maths-
If ax=b, by=c and cz =a then prove that xyz=1.
If ax=b, by=c and cz =a then prove that xyz=1.
Maths-General
Maths-
You can rent books at a local store for $5.00 each. An Internet company offers a flat fee of $20.00 per month for as many books as you want. How many books do you need to rent to make the online rental a better buy?
You can rent books at a local store for $5.00 each. An Internet company offers a flat fee of $20.00 per month for as many books as you want. How many books do you need to rent to make the online rental a better buy?
Maths-General
Maths-
Manoj has a set of blocks that are of the same height. The cone shaped block has a volume of 125 cubic inches. The sphere-shaped block has a volume of 250 cubic inches. What do you know about the radius of the base cone – shaped block?
Manoj has a set of blocks that are of the same height. The cone shaped block has a volume of 125 cubic inches. The sphere-shaped block has a volume of 250 cubic inches. What do you know about the radius of the base cone – shaped block?
Maths-General
Maths-
The slope of a line is –½ and it passes through origin. Find its equation.
The slope of a line is –½ and it passes through origin. Find its equation.
Maths-General
Maths-
A water pipe is a cylinder 30 inches long, with a radius of 1 inch. At one end of the cylinder there is a hemisphere. What is the volume of the water pipe?
A water pipe is a cylinder 30 inches long, with a radius of 1 inch. At one end of the cylinder there is a hemisphere. What is the volume of the water pipe?
Maths-General
Maths-
The graph shows the subscription cost to a certain club in town. Write an equation of the
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
The graph shows the subscription cost to a certain club in town. Write an equation of the
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
Maths-General
Maths-
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.
Maths-General
Maths-
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x.
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x.
Maths-General
Maths-
Find the equation of line such that its y-intercept is 20 and slope is ½.
Find the equation of line such that its y-intercept is 20 and slope is ½.
Maths-General
Maths-
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?
Maths-General
Maths-
The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
Maths-General